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Results tagged with differential-topology
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user 104774
The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
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Homotopy type of $SO(4)/SO(2)$
A classical result states that the quotient $SO(4)/SO(3)$ is homotopy equivalent to $S^3$. In fact, this can be stated in more general terms since $SO(n+1)/SO(n)$ has the homotopy type of $S^n$. What …
- 325
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On the homotopy type of $\mathrm{Diff}(\mathbb{S}^3)$
I am confused with the following argument. I know I am doing something wrong but I can't find my mistake.
On one hand, one knows that if $M$ is a Lie group, then
$$\mathrm{Diff}(M)\simeq M\times\mathr …
- 325